Bulletin Math 58

BULLETIN

No. 58 June 2006

The ICMI Bulletin is produced and distributed

with the financial support of Universit Laval, Qubec, Canada.

Bulletin of the International Commission on

Mathematical Instruction

No. 58 June 2006

Editor:

Bernard R. Hodgson Dpartement de mathmatiques et de statistique

Universit Laval Qubec G1K 7P4 CANADA

Table of Contents About ICMI 1 The Members of ICMI 3 ICMI Executive Committee 2003-2006 4 The ICMI Awards for 2005 (Press release) 6 ICME-9 Proceedings: The Revised Version of the CD Issued 11 Bernard R. Hodgson Election of the 2007-2009 Executive Committee of ICMI The Slate of Candidates 13 Bernard R. Hodgson A Call for Bids for ICME-12 (2012) A Reminder 14 Bernard R. Hodgson IMU President Receives a Knighthood 14 Celebrating the ICMI Centennial 15 A Change in the Web Address of ICME-10 15 Morten Blomhj Purchasing the NISS Volumes: A New Procedure for the ICMI Discount 16 A New ICMI Study Volume Available NISS 9 17 Report on ICMI Activities in 2005 21 Bernard R. Hodgson ICMI Accounts 2005 27 Bernard R. Hodgson A Report from HPM 30 Constantinos Tzanakis

ICMI Affiliated Study Groups Websites 34 A Report from WFNMC 35 Petar S. Kenderov Announcement of a New Publication on PME Research 37 A Report on the 10th ICMI Study: The Role of the History of Mathematics in the Teaching 38 and Learning of Mathematics Fulvia Furinghetti In Memoriam Shokichi Iyanaga (1906-2006) 45 Hyman Bass, Bernard R. Hodgson and Shigeru Iitaka A Call for Papers IJSME 49 Building Bridges between Theoretical Frameworks in Mathematics Education 50 Michle Artigue and Bernard R. Hodgson Twenty-Five Years of the Didactic Transposition 51 Marianna Bosch and Josep Gascn The International Centre for Pure and Applied Mathematics (CIMPA) and Mathematics 66 within Developing Countries Michel Jambu LEnseignement Mathmatique Now Available on the Web 71 ICMI on the Web 71 Three New Journals Related to Mathematics Education 72 AMUCHMA Newsletter on the History of Mathematics in Africa 73 ICMI Activities on the Web 75 A Note on Copyright 75 Conferences on Technology in Mathematics Education 75 Future Conferences 76 ICMI Representatives 89

ICMI Bulletin No. 58 1 June 2006

About ICMI Background The International Commission on Mathematical Instruction, ICMI, is a commission of the International Mathematical Union (IMU), an international nongovernmental and nonprofitmaking scientific organisation with the purpose of promoting international cooperation in mathematics. Among international organisations devoted to mathematics education, ICMI is distinctive because of its close ties to both the mathematics and the mathematics education professional communities, as well as for its breadth thematic, cultural, and regional. Established at the Fourth International Congress of Mathematicians held in Rome in 1908 with the initial mandate of analysing the similarities and differences in the secondary school teaching of mathematics among various countries, ICMI has expanded its objectives and activities considerably over the years. The Commission aims to offer educational researchers, curriculum designers, educational policy makers, teachers of mathematics, mathematicians, mathematics educators and others interested in mathematical education, a forum to promote reflection, collaboration, exchange and dissemination of ideas and information on all aspects of the theory and practice of contemporary mathematical education from an international perspective. ICMI thus takes initiatives in inaugurating appropriate programmes designed to further the sound development of mathematical education at all levels, and to secure public appreciation of its importance. The Commission is also charged with the conduct of the activities of IMU bearing on mathematical or scientific education. In the pursuit of its objectives, the Commission cooperates with various groups, regional or thematic, which may be formed within or outside its own structure. As a scientific union, IMU is a member organisation of the International Council for Science (ICSU). This implies that ICMI, through IMU, is to abide to the ICSU statutes, one of which establishes the principle of non-discrimination. This principle affirms the right and freedom of scientists to associate in international scientific activities regardless of citizenship, religion, political stance, ethnic origin, sex, and suchlike. Apart from observing general IMU and ICSU rules and principles, ICMI works with a large degree of autonomy. Structure Members of ICMI are not individuals but countries, namely those countries that are members of IMU and other countries specifically coopted to the Commission. Each member of ICMI appoints a Representative and may create a Sub-Commission for ICMI to maintain liaison with the Commission in all matters pertinent to its affairs. ICMI currently has 81 members. The Commission is administered by the Executive Committee (EC) of ICMI, elected by the General Assembly of IMU and responsible for conducting the business of the Commission in accordance with its Terms of Reference and subject to the direction and review of the members. The General Assembly of ICMI, consisting of the members of the ICMI EC and the Representatives to ICMI, convenes every four years in conjunction with the International Congress on Mathematical Education. ICMI Activities A major event in the life of the international mathematics education community, the quadrennial International Congress on Mathematical Education, ICME, is held under the auspices of ICMI and typically gathers more than three thousand participants from all over the world. The


ICMI Executive Committee is responsible for the selection of a site for an ICME as well as for the appointment of an International Programme Committee, in charge of the scientific content of the congress. The practical and financial organisation of an ICME is the independent responsibility of a Local (or National) Organising Committee, under the observation of general ICMI principles. Apart from the ICME congresses, the Commission organises or supports various activities, such as the ICMI Study Programme, in which each Study, built around an international study conference, addresses an issue or topic of particular significance in contemporary mathematics education and is directed towards the preparation of a volume, published in the New ICMI Study Series (NISS), which aims to offer a coherent, state-of-the art representation of the domain of the Study; the ICMI Regional Conferences, supported by ICMI morally and sometimes financially in order to facilitate the organisation of regional meetings on mathematics education, especially in less affluent parts of the world; or the ICMI Solidarity Project, aiming at increasing the commitment and involvement of mathematics educators around the world in order to help the furtherance of mathematics education in those parts of the world where there is a need for it that justifies international assistance and where the economic and socio-political contexts do not permit adequate and autonomous development. The above-mentioned activities are of a more or less regular nature. In addition to those, ICMI involves itself in other activities on an ad hoc basis. For instance, ICMI has recently reinitiated contacts with UNESCO. Also ICMI is involved in the planning of the education components on the programme of the International Congresses of Mathematicians, the ICMs. ICMI Affiliated Study Groups The Commission may approve the affiliation to ICMI of Study Groups, focussing on a specific field of interest and study in mathematics education consistent with its aims. The current Study Groups affiliated to ICMI are the International Study Group on the Relations between the History and Pedagogy of Mathematics (HPM), the International Study Group for Mathematical Modelling and Applications (ICTMA), the International Organization of Women and Mathematics Education (IOWME), the International Group for the Psychology of Mathematics Education (PME) and the World Federation of National Mathematics Competitions (WFNMC). Information and Communication The official organ of ICMI since its inception is the international journal LEnseignement Mathmatique, founded in 1899. The homepage of the journal can be found at the address http://www.unige.ch/math/EnsMath/. Under the editorship of the Secretary-General, ICMI publishes the ICMI Bulletin, appearing twice a year. The Bulletin is accessible on the ICMI website http://www.mathunion.org/ICMI/, where more information about ICMI can also be found. Support to ICMI The principal source of ICMIs finances is the support it receives from its mother organisation, the International Mathematical Union. Every year ICMI thus has to file a financial report for the endorsement of IMU, as well as a scientific report on its activities. Quadrennial reports are presented to the General Assemblies of both IMU and ICMI. But one of the greatest strengths of ICMI is the time contributed freely by the hundreds of mathematicians and mathematics educators committed to the objectives of the Commission.


The Members of ICMI

All countries members of the International Mathematical Union, the mother organisation of ICMI, are de facto members of ICMI. But it is also possible for a country not a member of IMU to become a member of ICMI. (Information on this matter can be obtained from the Secretary-General of ICMI.) There are currently 81 member countries of ICMI, 67 of which are also members of IMU. In the following list, (*) indicates a member of ICMI that is not a member of IMU. A Argentina Armenia Australia Austria B Bangladesh (*) Belgium Bosnia and Herzegovina Botswana (*) Brazil Brunei Darussalam (*) Bulgaria C Cameroon Canada Chile China Costa Rica (*) Croatia Cuba Czech Republic D Denmark E Egypt Estonia F Finland France G Georgia Germany Ghana (*) Greece

H Hong Kong Hungary I Iceland India Indonesia Iran Ireland Israel Italy Ivory Coast J Japan K Kazakhstan Republic of Korea Kuwait (*) L Latvia Lithuania Luxembourg (*) M Malawi (*) Malaysia (*) Mexico Mozambique (*) N Netherlands New Zealand Nigeria Norway P Pakistan Peru Philippines

Poland Portugal R Romania Russia S Saudi Arabia Senegal (*) Serbia and Montenegro Singapore Slovakia Slovenia South Africa Spain Swaziland (*) Sweden Switzerland T Thailand (*) Tunisia Turkey U Ukraine United Kingdom United States of America Uruguay V Venezuela Vietnam Z Zambia (*)


The International Commission on Mathematical Instruction

ICMI Executive Committee 2003 2006

President: Hyman BASS 2413 School of Education 610 E. University University of Michigan Ann Arbor, MI 48109-1259 USA [email protected] Vice-Presidents: Jill ADLER School of Education University of the Witwatersrand Private Bag 3, P.O. Wits, 2050 Johannesburg, SOUTH AFRICA [email protected] Michle ARTIGUE IREM, Case 7018 Universit de Paris VII 2 place Jussieu 75251 Paris - Cedex 05, FRANCE [email protected] Secretary-General: Bernard R. HODGSON Dpartement de mathmatiques et de statistique Universit Laval Qubec G1K 7P4 CANADA [email protected] Members-at-Large: Carmen BATANERO Facultad de Ciencias de la Educacin Universidad de Granada Campus de Cartuja 18071 Granada, SPAIN [email protected] Maria FALK DE LOSADA Rectora Universidad Antonio Nario Bogot, COLOMBIA [email protected]


Nikolai DOLBILIN Steklov Mathematical Institute Gubkin str. 8, GSP-1 Moscow 117966, RUSSIA [email protected] Peter L. GALBRAITH School of Education The University of Queensland St Lucia, QLD 4072 AUSTRALIA [email protected] Petar S. KENDEROV Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev Street, Block 8, 1113 Sofia, BULGARIA [email protected] Frederick Koon-Shing LEUNG Faculty of Education The University of Hong Kong Pokfulam Road, HONG KONG SAR [email protected] Ex officio members: John M. BALL (President of IMU) Mathematical Institute University of Oxford 24-29 St Giles Oxford, OX1 3LB, UK [email protected] Phillip GRIFFITHS (Secretary of IMU) Institute for Advanced Study Olden Lane Princeton, NJ 08540-0631 USA [email protected]

Legend: IMU stands for the International Mathematical Union. ICMI is a commission of IMU.


The ICMI Awards for 2005

The Felix Klein and Hans Freudenthal Medals are the two awards created by the International Commission on Mathematical Instruction (ICMI) for recognising outstanding achievement in mathematics education research. The Felix Klein Medal, named for the first president of ICMI (1908-1920), honours a lifetime achievement. The Hans Freudenthal Medal, named for the eight president of ICMI (1967-1970), recognises a major cumulative program of research. The ICMI Awards represent the judgement of an (anonymous) jury of distinguished scholars of international stature. The jury for the 2005 Awards was chaired by Professor Michle Artigue, of the Universit de Paris 7. ICMI is proud to announce the second awardees of the Klein and Freudenthal Medals.

The Felix Klein Medal for 2005 is awarded to Ubiratan DAmbrosio, Emeritus Professor at UNICAMP, in Brasil. This distinction acknowledges the role Ubiratan DAmbrosio has played in the development of mathematics education as a field of research and development throughout the world, above all in Latin America. It also recognises Ubiratan DAmbrosios pioneering role in the development of research perspectives which are sensitive to the characteristics of social, cultural, and historical contexts in which the teaching and learning of mathematics take place, as well as his insistence on providing quality mathematics education to all, not just to a privileged segment of society. The Hans Freudenthal Medal for 2005 is awarded to Paul Cobb, Professor at Vanderbilt University, in the US. This distinction acknowledges his outstanding contribution to mathematics education: a rare combination of theoretical developments, empirical research and practical applications, which has had a major influence on the mathematics education community and beyond.

Citations of the work of these medallists can be found below. Presentation of the medals, and invited addresses of the medallists, will occur at ICME-11 in Monterrey, Mxico, July 2008. Recipients of previous ICMI Awards: 2003 Felix Klein Medal Professor Guy Brousseau 2003 Hans Freudenthal Medal Professor Celia Hoyles (Document for a press release issued on April 3, 2006)


Citation for the 2005 ICMI Felix Klein Medal to

Professor Ubiratan DAmbrosio

The second Felix Klein Medal of the International Commission on Mathematical Instruction (ICMI) is awarded to Professor Ubiratan DAmbrosio, Brasil. This distinction acknowledges the role Ubiratan DAmbrosio has played in the development of mathematics education as a field of research and development throughout the world, above all in Latin America. It also recognises Ubiratan DAmbrosios pioneering role in the development of research perspectives which are sensitive to the characteristics of social, cultural, and historical contexts in which the teaching and learning of mathematics take place, as well as his insistence on providing quality mathematics education to all, not just to a privileged segment of society. His role in promoting mathematics education research and development in Latin America, both as regards priorities and content and as regards institutional and organisational frameworks, can hardly be over-estimated. His focus on providing graduate and postgraduate programmes for young researchers exemplifies his contribution.

Ubiratan DAmbrosio was born in 1932 in So Paulo, Brazil. He was trained as a mathematician in Brazil and Italy and obtained his doctorate in science at the University of So Paulo in 1963. Until 1972 he spent most of his time in the USA (Brown University, SUNY/Buffalo) where he worked on Calculus of Variations and Measure Theory, while at the same time developing an increasing interest in interdisciplinary work and postgraduate programmes. Upon his return to Brazil in 1972, when he took up the post of director of the Institute of Mathematics, Statistics and Computer Sciences at the State University of Campinas (UNICAMP), Ubiratan DAmbrosios endeavour was to include new topics such as mathematical logic, mathematical modelling, bio-mathematics, computational linguistics and artificial intelligence as part of the Institutes research profile along with more classical areas. Later, he broadened his contribution to include mathematics education. In 1975 he was involved in creating a Masters programme in the teaching of sciences and mathematics at the UNICAMP. During the 1970s, Ubiratan DAmbrosio gradually moved into the field of mathematics education, partly as a result of his involvement in the activities of the Inter-American Committee on Mathematics


Education (IACME/CIAEM), of which he was later to become Vice-President and President. This gave rise to a variety of contacts with international protagonists in mathematics education such as Luiz Santal, Hans Freudenthal, and Ed Begle, contacts which were greatly extended and amplified by his attendance at the International Congresses on Mathematical Education (ICMEs), in particular ICME-3, held in Karlsruhe, Germany in 1976. For that Congress he was in charge of a panel working on the theme Why teach mathematics?, the report of which (Overall goals and objectives for mathematical education) was published with DAmbrosio as the author in Unescos New trends in mathematics teaching, Vol. IV (Paris, 1979). At ICME-3 he raised, as one of the very first mathematics educators to do so, socio-cultural questions related to research in mathematics education while pointing to the links between these questions and the history of mathematics and the other sciences in different contexts. Ubiratan DAmbrosio was elected Vice-President of ICMI for the term 1979-1983, in which capacity he helped found the African Mathematical Union and the African Society for the Advancement of Science. When his term was over he took up office as the chair of the International Study Group of the Relations between History and Pedagogy of Mathematics. As a result of his interest in the social and cultural conditions for mathematics education, in particular as regards the nature of mathematical knowledge in different cultures at different times, Ubiratan DAmbrosio began to develop what is internationally his best-known contribution to the field of mathematics education, the idea of ethnomathematics. In 1978 he wrote a paper on the mathematical knowledge and practices of native American cultures, took part in a Unesco conference in Khartoum, Sudan, on developing mathematics in third world countries, and participated in a conference Mathematics and the Real World at Roskilde University, Denmark. Probably the first international presentation of his ideas concerning ethnomathematics, including a sketch of its development into a programme of research and activity, was Ubiratan DAmbrosios plenary lecture Socio-Cultural Bases for Mathematical Education at ICME-5 in Adelaide in 1984. Soon after came a series of publications that developed the initial ideas in greater detail, and in 1985 he co-founded the International Study Group on Ethnomathematics. He was the Vice-President of the study group 1988-1996. Since its inception, ethnomathematics has continued to grow as a field of research and development and has exerted considerable influence on mathematics education in several continents, above all in Latin America and Africa. Today, Ubiratan DAmbrosio is a very active Emeritus Professor at UNICAMP while also teaching at several other universities in So Paulo in postgraduate programmes of mathematics education and the history of science. He also continues to do research in ethnomathematics and related areas. Ubiratan DAmbrosio belongs to a generation that helped to found the field of mathematics education. His contribution to research is essentially as a philosopher in the classical broad sense of that word of mathematics education reflecting on its role in a complex world characterised by unrest and by an uneven distribution of goods and privileges across regions, countries, and societies. By focusing his attention on developing cultures, Ubiratan D'Ambrosio broadened our conception of mathematics education. More than that, he has helped to open the eyes of the mathematics education community to an understanding of how mathematical ideas are generated and how they evolved through the history


of mankind. This work made a significant contribution to our appreciation of the field of scientific invention and its relation to ad hoc practices that occur in different cultures and subcultures. His contribution has played a key role in legitimating alternative forms of mathematical activity and in elaborating the now-familiar idea that the quasi-mathematical knowledge of the learner can be built upon rather than rejected. (Document for a press release issued on April 3, 2006)

Citation for the 2005 ICMI Hans Freudenthal Medal to Professor Paul Cobb

The second Hans Freudenthal Medal of the International Commission on Mathematical Instruction (ICMI) is awarded to Professor Paul Cobb, whose work is a rare combination of theoretical developments, empirical research and practical applications. His work has had a major influence on the mathematics education community and beyond. Born in a small town in southern England, Paul Cobb did not expect to develop an academic career. After earning a BSc with honours in mathematics from the University of Bristol, he spent a few years working as a secondary school mathematics teacher. In 1978 he enrolled into a one-year Masters programme in mathematics education at the University of Georgia in Athens. Little did he know at that time where this seemingly insignificant step would take him. A few years later he was already one of the rising stars of research in mathematics education. It did not take him much longer to gain an international recognition and become a central figure as well as a major influence in the field of mathematics education. He is now Professor at Vanderbilt University, in the US.


Paul Cobbs professional activity spans two decades and more than one research paradigm. Once a close collaborator of Ernst von Glasersfeld and of Leslie P. Steffe, he began his career as a developer, and subsequently a critic, of the theoretical perspective known as radical constructivism. Cobbs research and development projects, first in the field of elementary school mathematics and later of middle school statistics, are exemplary in many respects. They are a product of a comprehensive, well-designed, consistent, and constantly updated research programme. Its main strength is its sensitivity, both to the lessons learned from earlier implementations and to the evolving practical needs of the field of education. The dynamic character of Paul Cobb's theoretical perspective is a natural outcome of his thoughtful studies. His work shows an acute awareness of the insufficiency of any over-delineated approach, and he has gradually moved the focus of his work from individual learners to teams, to classrooms, and to district-wide infrastructure. Across these settings, he has been systematically examining the consequences of the assumption that human learning is inherently social. In this respect, his work with Erna Yackel on sociomathematical norms paved important new ground. Thanks to this systematic foundational contribution, Paul Cobb is today regarded as one of the leading sociocultural theorists in the field of mathematics education and beyond, and his work is currently yielding new insights on issues such as equity and students identities. Paul Cobb is a prolific writer, widely read within the broad education community. His research spans more than a hundred journal articles and book chapters, as well as several books authored or edited with others. Prestigious journals, such as Educational Researcher, Cognition & Instruction, Journal of the Learning Sciences, Mind, Culture, and Activity have consistently published his work. Many of his publications have multiple authors, as do his numerous empirical studies. Paul Cobbs life project can thus be seen as a truly collective endeavour, implemented according to the same principles as those that he promotes in his educational writings. Paul Cobbs work has had a tangible impact on the mathematics education vocabulary. It is through this work that such widely-used notions as taken-as-shared meaning or sociomathematical norms entered the professional discourse. The fact that his contribution is recognized and valued within the mathematics education community and beyond finds further confirmation in his numerous grants, distinctions and awards, and in particular, his recent election to the National Academy of Education of the US. (Document for a press release issued on April 3, 2006)


ICME-9 Proceedings: The Revised Version of the CD Issued Due to a defect in the content of the CD accompanying the book of Proceedings of ICME-9, it was announced in the ICMI Bulletin 55 (December 2004), p. 6, that the Japanese colleagues in charge of the congress had decided to issue a revised and expanded version of the CD, to be sent to all ICME-9 participants. The appearance of the revised version of the CD (r-CD) has met with some delay with respect to the original plans, and this has been a matter of deep regret and serious concern to our Japanese friends. But I am pleased, on behalf of the organisers of ICME-9, to inform the ICMI community that the process of preparation of the r-CD is now completed and that the shipping of the new CD is planned to take place by the end of June 2006. The list of the regular lectures presented at ICME-9 and included in the revised CD is given in the ICMI Bulletin 57 (December 2005). The following text is the preface appearing on the r-CD. Bernard R. Hodgson Secretary-General of ICMI

Preface (taken from the r-CD)

The book of Proceedings of ICME-9,

Proceedings of the Ninth International Congress on Mathematical Education, Hiroshi Fujita, Yoshihiko Hashimoto, Bernard R. Hodgson, Peng Yee Lee, Stephen Lerman and Toshio Sawada, eds., Kluwer Academic Publishers, 2004,

was published accompanied by a CD. Regrettably, that CD suffered from some serious omissions, corrected in the present revised edition. The two main additions to this Digital Edition (Revised 2005) of the Proceedings of the Ninth International Congress on Mathematical Education are: (i) thirty-three of the papers presented as regular lectures at ICME-9 (for a total of 488 pages), (ii) the entire book of Proceedings, reproduced here with kind permission of the copyright owner, Springer Science + Business Media. This revised CD (r-CD) is divided in three parts. The first part presents various materials newly compiled for this expanded digital edition. Besides buttons allowing navigation throughout the r-CD, this part provides the welcome greetings of the Chair of the International Programme Committee presented at the opening ceremony of ICME-9, as well as the list of the members of the ICMI


Executive Committee and of the ICME-9 International Programme Committee and National Organizing Committee. But more importantly one finds there the texts from thirty-three of the regular lecturers, and also a set of photographs from the congress, many of which were taken during the opening ceremony. The second part of this r-CD repeats the contents of the original CD, and the third part is a file corresponding to the entire book version of the ICME-9 Proceedings, not previously available electronically. It is hoped that the Proceedings of the Ninth International Congress on Mathematical Education Digital Edition (Revised 2005) will be a useful tool for researchers as well as for all those interested in mathematics education, while providing a more complete and vivid record of the congress itself. To understand what this r-CD has accomplished, we briefly recount the story of the original. While it is stated in the Preface of the printed Proceedings (p. xii) that the CD part of these Proceedings contains, in addition to files for the whole content of the book part, vivid scenes of the ceremonies and the IRT, full texts of regular lectures if available, and some scientific animation etc., it turned out that neither the whole content of the book part nor the full texts of the regular lectures if available appear on the accompanying original CD. The editors of the Proceedings, the Japanese organizers of the ICME-9 congress and the Executive Committee of ICMI deeply deplore this regrettable situation, which obviously was a source of frustration to many participants and especially to the regular lecturers, whose papers thus remained inaccessible to the community. However the organizers of the congress announced, shortly after the proceedings volume came out, their decision to publish a revised and expanded version of the CD to be sent anew to all ICME-9 participants. On behalf of my colleagues of the Executive Committee of ICMI, I wish to express our gratitude to all the Japanese colleagues who, a number of years after the conclusion of the congress, have worked together in identifying and implementing a sound solution to the problem caused by the defect in the original ICME-9 CD. We are in particular grateful to Katsuhiko Shimizu, who brought an essential contribution in the preparation and production of the expanded CD. But above all we wish to repeat here our highest esteem and appreciation to the Chair of the International Programme Committee and President of the National Organizing Committee, Hiroshi Fujita San. During the closing ceremony of ICME-9, the President of ICMI and myself already had the opportunity to tangibly express to our colleague our gratitude for the exceptional leadership role he had played in the organisation of ICME-9. The resolution of the flaw in the first version of the CD owes much to his professionalism and sensibility. Bernard R. Hodgson Secretary-General of ICMI [email protected] December 2005


Election of the 2007-2009 Executive Committee of ICMI The Slate of Candidates

The Executive Committee of the International Mathematical Union has announced in April 2006 the composition of the slate of candidates for the election of the next ICMI Executive Committee:

President: Michle Artigue (France) Secretary-General: Bernard R. Hodgson (Canada) Vice Presidents: Jill Adler (South Africa) William (Bill) Barton (New Zealand) Members-at-Large (7 candidates for 5 posts): Maria G. (Mariolina) Bartolini Bussi (Italy) Jaime Carvalho e Silva (Portugal) Olimpia Figueras (Mexico) Celia Hoyles (UK) S. Kumaresan (India) Frederick K.S. Leung (Hong Kong) Alexei Semenov (Russia)

The election of the 2007-2009 ICMI EC will take place during the General Assembly of IMU, to be held in August 2006 in Santiago de Compostela, Spain, on the occasion of ICM-2006 (Madrid). As announced earlier (see ICMI Bulletin 55, December 2004, pp. 18-22), this IMU GA will also be presented with amendments to the procedure for the election of the ICMI EC. One consequence, should these amendments be adopted, is that the following election of the ICMI EC would happen during the General Assembly of ICMI that will take place in 2008 on the occasion of ICME-11. Thus, as a transition measure, the next ICMI EC would serve for a three-year term (2007-2009), instead of the usual four-year. Considering the procedure for election currently in force, the above slate is being formally submitted by the IMU Executive Committee to the IMU GA. Still the proposed new model for the preparation of the ICMI EC slate, including the formation and action of an ICMI Nominating Committee with mandate to prepare this slate, has been implemented for the 2006 election. The slate submitted by the 2006 ICMI Nominating Committee had the status of advice to the IMU EC. The reader is reminded that 2006 ICMI Nominating Committee is composed as follows: Mogens Niss (Chair, Denmark), John Ball (IMU President, UK), Hyman Bass (ICMI President, USA), Victor Vassiliev (Russia), Tomas Recio (Spain), Gnter Trner (Germany) and Lim-Teo Suat Khoh (Singapore). Bernard R. Hodgson, Secretary-General of ICMI [email protected]


A Call for Bids for ICME-12 (2012) A Reminder

A call for bids to host the Twelfth International Congress on Mathematical Education (ICME-12), to take place in 2012, was issued in the December 2004 ICMI Bulletin (No. 55, pp. 11-12). ICMI member countries were then invited to indicate, by November 1, 2005, their intention to submit a bid for ICME-12. Three countries have responded to this call, namely (in alphabetical order) China, Korea and South Africa. While this preliminary declaration does not imply that these three countries should feel obliged to eventually present a firm bid, I also with to stress that at this stage it is possible for other countries to submit a bid, even if no preliminary declaration has been made. I wish to remind that the final deadline for submitting a bid is November 1, 2006. Documents should be presented in twelve copies. Decisions about the site of ICME-12 will be made by the 2007-2009 Executive Committee of ICMI, to take charge as of January 1, 2007. I shall be happy to reply to any query about preparing an invitation to host ICME-12 (or a later ICME...). Bernard R. Hodgson, Secretary-General of ICMI [email protected]

IMU President Receives a Knighthood IMU President John Ball, Sedleian Professor of Natural Philosophy and Fellow of Queen's College, University of Oxford, has received a knighthood in the New Year (2006) Honours list. A world-renowned mathematician, John Ball is particularly active, through his IMU presidency, in supporting the advancement of mathematics in developing countries. His main research areas lie in elasticity theory, the calculus of variations, and infinite-dimensional dynamical systems. He is especially interested in the mathematics of microstructure arising from phase transformations in solids, where the problem of predicting microstructure morphology is related to deep unsolved questions of the multi-dimensional calculus of variations such as understanding quasiconvexity. (Based on a BBC News communiqu, December 31, 2005)


Celebrating the ICMI Centennial

ICMI will be celebrating in 2008 its 100th anniversary. The International Programme Committee appointed to plan the symposium organised on this occasion, whose composition was announced in the June 2005 issue of the ICMI Bulletin (No. 56), had its first meeting in February 2006 under the chairmanship of Ferdinando Arzarello ([email protected]). Details on the programme of the symposium will be announced in a near future. But it is already known that the symposium will take place in Rome the birthplace of ICMI on March 5-8, 2008, at the Accademia dei Lincei for the first days, and on the final day at Liceo Virgilio, an ancient school very near to Lincei. The Local Organising Committee is chaired by Marta Menghini ([email protected]).

A Change in the Web Address of ICME-10 Note of the Editor: The following message was sent by e-mail on May 31, 2006, to all the participants at ICME-10. Since the early years of the planning of the ICME-10, our website (www.icme-10.dk) has generously been hosted by the Southern University of Denmark. However, due to some structural changes at the university, our domain was left unprotected for a short period of time. It was a surprise and a shock to realize that the domain www.ICME-10.dk had in the meantime been bought by an unidentified person or organisation. We have therefore been forced to change our domain to:

www.icme10.dk (We have simply lost our hyphen!) We will of course make an effort to recover our old domain and establish a link, so that both addresses will hopefully be active in the future. Meanwhile, please use our new address. Fortunately all the web-pages of the sub-groups are fully updated and the procedure for uploading documents to these pages is unchanged. So the functioning of the website is the same. We apologise for any inconvenience this change of domain may cause. As promised at ICME-10 the website will remain active until at least a year after ICME-11 hopefully without further changes in the domain. Morten Blomhj, Chair of Local Organising Committee for ICME-10 IMFUFA, Roskilde University, DENMARK [email protected]


Purchasing the NISS Volumes: A New Procedure for the ICMI Discount

The volumes resulting from the ICMI Studies appear in the New ICMI Study Series (NISS), published by Springer under the general editorship of the President and Secretary-General of ICMI. According to the contract negotiated in 1999 between ICMI and Springer (then Kluwer), any individual interested in the activities of ICMI and purchasing these books for personal use is entitled to the ICMI Society Discount, namely a 60% discount on all NISS series hardbound volumes and a 25% discount on all softbound volumes within the series. Springer has recently announced a new procedure for obtaining the ICMI society discount. Orders must be placed personally through the NISS homepage

http://www.springeronline.com/series/6351 on the Springer website. In order to obtain the society discount granted to ICMI, individuals should enter the respective tokens when asked to during the ordering process, on the bottom of the payment screen. The following ICMI Token Numbers have been issued by Springer:

Token for Hardbound: YSwE925dq6SEdhk Token for Softbound: C6zHr25NZDdFAay

This discount is not available to institutions or when ordering the NISS volumes through a bookstore. (Note: Springer uses the expression ICMI members when speaking of their potential customers in this specific context, which neglects the fact that ICMI members are countries, not individuals.) Address of the NISS homepage

http://www.springeronline.com/series/6351


A New ICMI Study Volume Available NISS 9

The Study volume resulting from the thirteenth ICMI Study has recently appeared as volume 9 of the New ICMI Study Series (NISS):

Frederick K.S. Leung, Klaus-D. Graf and Francis J. Lopez-Real, eds., Mathematics Education in Different Cultural Traditions A Comparative Study of East-Asia and the West: The 13th ICMI Study. Springer, 2006. 597 p. (NISS 9) ISBN: 0-387-29722-7

Individuals purchasing the book for personal use are entitled to the usual ICMI discount of 60% on the hardbound price. More information about the book can be found on the NISS homepage, inside Springer website:

http://www.springeronline.com/series/6351 From the back cover In recent years there has been an upsurge of interest concerning international comparisons of mathematics education, stimulated in part by large-scale studies such as TIMSS and PISA. However, many educators have felt that the analysis of such comparisons requires a deep understanding of the underlying cultural and social factors involved, and this perspective led to the 13th ICMI Study Conference being convened to consider the issues. Because of the impossible complexity of trying to cover all different cultural traditions worldwide it was decided to focus on two significant traditions, broadly speaking East Asia and the West. This important volume is the outcome of the ICMI Study. The volume covers a very wide field including the contexts of mathematics education, the curriculum, teaching and learning, and teachers values and beliefs. Within these broad parameters some of the particular cross-cultural issues that are discussed include intuition and logical reasoning, influences of Confucianism and Ancient Greek traditions, basic skills and process abilities, learners perspectives, assessment practices, textbooks and ICT multimedia. Throughout the book emphasis is placed on uncovering and understanding differences and similarities, not just between these two major traditions but within the cultures themselves. Simplistic analyses or solutions are avoided and the authors demonstrate a cultural sensitivity that results in a collaborative, rather than competitive, spirit evident in the comparisons that are made. Much of the focus is on learning together, as much from our failures as our successes. The contributing authors are highly experienced and eminent members of the mathematics education community and together they have provided us with a book that is an invaluable source of information, discussion, reflection and insight. Mathematics Education in Different Cultural Traditions will be of special interest to mathematics teachers, teacher educators, researchers, education administrators, curriculum developers, and student teachers.


Table of Contents Preface Mathematics Education in Different Cultural Traditions: A Comparative Study of East Asia and the

West Discussion Document Mathematics Education in East Asia and the West: Does Culture Matter? LEUNG Koon Shing Frederick Section 1: Context of Mathematical Education Introduction FAN Lianghuo & Walther FISCHER Chapter 1-1 : A Traditional Aspect of Mathematics Education in Japan Ichiei HIRABAYASHI Chapter 1-2: From Wasan to Yozan Kenji UENO Chapter 1-3: Perceptions of Mathematics and Mathematics Education in the Course of History A

Review of Western Perspectives Christine KEITEL Chapter 1-4: Historical Topics as Indicators for the Existence of Fundamentals in Educational

Mathematics Walther L. FISCHER

Chapter 1-5: From Entering the Way to Exiting the Way: In Search of a Bridge to Span Basic Skills and Process Abilities

WONG Ngai-Ying Chapter 1-6: Practice Makes Perfect: A Key Belief in China LI Shiqi Chapter 1-7: The Origins of Pupils Awareness of Teachers Mathematics Pedagogical Values:

Confucianism and Buddhism-Driven LEU Yuh-Chyn & WU Chao-Jung Section 2: Curriculum Introduction Margaret WU, PARK Kyungmee & LEUNG Koon Shing Frederick Chapter 2-1: Some Comparative Studies between French and Vietnamese Curricula Annie BESSOT & Claude COMITI Chapter 2-2: An Overview of the Mathematics Curricula in the West and East Margaret WU & ZHANG Dianzhou Chapter 2-3: Classification and Framing of Mathematical Knowledge in Hong Kong, Mainland China,

Singapore, and the United States LI Yeping & Mark B. GINSBURG


Chapter 2-4: Comparative Study of Arithmetic Problems in Singaporean and American Mathematics Textbooks

YEAP Ban-Har; Beverly J. FERRUCCI & Jack A. CARTER Chapter 2-5: A Comparative Study of the Mathematics Textbooks of China, England, Japan, Korea,

and the United States PARK Kyungmee & LEUNG Koon Shing Frederick Chapter 2-6: A Comparison of Mathematics Performance between East and West: What PISA and

TIMSS Can Tell Us Margaret WU Chapter 2-7: Case Studies on Mathematics Assessment Practices in Australian and Chinese Primary

Schools ZHAO Da-Cheng; Joanne MULLIGAN & Michael MITCHELMORE Chapter 2-8: Philippine Perspective on the ICMI Comparative Study Bienvenido F. NEBRES, S.J. Section 3: Teaching and Learning Introduction Colette LABORDE Chapter 3-1: The TIMSS 1995 and 1999 Video Studies Johanna NEUBRAND Chapter 3-2: Proposal for a Framework to Analyse Mathematics Education in Eastern and Western

Traditions Gabriele KAISER, Keiko HINO AND Christine KNIPPING Chapter 3-3: Cultural Diversity and the Learner's Perspective: Attending to Voice and Context David CLARKE, Yoshinori SHIMIZU, Soledad A. ULEP, Florenda L. GALLOS, Godfrey

SETHOLE; Jill ADLER & Renuka VITHAL Chapter 3-4: Mathematics Education in China: From a Cultural Perspective ZHENG Yuxin Chapter 3-5: Mathematics Education and Information and Communication Technologies: An

Introduction Klaus-Dieter GRAF Chapter 3-5a: Cultural Awareness Arising from Internet Communication between Japanese and

Australian Classrooms Masami ISODA; Barry McCRAE & Kaye STACEY Chapter 3-5b: The International Distance Learning Activities of HSARUC XU Fei Chapter 3-5c: Distance Learning between Japanese and German Classrooms Klaus-D. GRAF & Seiji MORIYA Section 4: Values and Beliefs Introduction Alan BISHOP


Chapter 4- 1 : Comparing Primary and Secondary Mathematics Teachers Beliefs about Mathematics, Mathematics Learning and Mathematics Teaching in Hong Kong and Australia

Bob PERRY, WONG Ngai-Ying & Peter HOWARD Chapter 4-2: The Impact of Cultural Differences on Middle School Mathematics Teachers Beliefs in

the U.S. and China AN Shuhua, Gerald KULM, WU Zhonghe, MA Fu & WANG Lin Chapter 4-3: U.S. and Chinese Teachers Cultural Values of Representations in Mathematics

Education CAI Jinfa Chapter 4-4: A Comparison of Mathematical Values Conveyed in Mathematics Textbooks in China

and Australia CAO Zhongjun, SEAH Wee TIONG & Alan J. BISHOP Chapter 4-5: Values and Classroom Interaction: Students Struggle for Sense Making Eva JABLONKA & Christine KEITEL Chapter 4-6: Trip for the Body, Expedition for the Soul: An Exploratory Survey of Two East Asian

Teachers of Mathematics in Australia SEAH Wee TIONG & Alan J. BISHOP Chapter 4-7: Conceptualising Pedagogical Values and Identities in Teacher Development CHIN Chien Section 5: Outlook and Conclusions Introduction LEUNG Koon Shing FREDERICK, Klaus-Dieter GRAF & Francis J. Lopez-Real Chapter 5-1: Elements of a Semiotic Analysis of the Secondary Level Classroom in Japan Carl WINSLW & Hideyo EMORI Chapter 5-2: Other Conventions in Mathematics and Mathematics Education Valeriy ALEKSEEV, Bill BARTON & Gelsa KNIJNIK Chapter 5-3: What Comes After This Comparative Study More Competitions or More

Collaborations? Alan J. BISHOP Index

The NISS 9 volume is available AT 60% DISCOUNT for individuals purchasing the book online on the Springer website

http://www.springeronline.com/series/6351 Please quote the ICMI Discount Token Number

YSwE925dq6SEdhk during the ordering process, on the bottom of the payment screen.


Report on

ICMI activities in 2005

1. Organisation The 2003-2006 Executive Committee (EC) of ICMI had its fourth and fifth meetings in 2005. The EC met on June 19-22, 2005, at the University of the Witwatersrand in Johannesburg, South Africa, just prior to the First Africa Regional Congress of ICMI. It also met on December 15-18, 2005, at the Indira Gandhi National Open University in New Delhi, India. A National Conference on Mathematics Education was held at the National Council of Educational Research and Training (NCERT), in New Delhi, in conjunction with the ICMI EC visit. The President and Secretary-General of ICMI were invited for part of the meeting of the Executive Committee of IMU held in Rio de Janeiro on April 22, 2005. In addition to allowing the IMU EC members to receive a report on ICMI and its activities, this meeting was the occasion of discussing specific issues such as the difficult financial situation of ICMI and the possible collaboration of ICMI to IMU initiative towards developing countries. It also allowed to examine concerns expressed by the IMU EC about the situation of students of mathematics at the university level and to identify a joint action of IMU and ICMI on this matter (see item 6 below). Following a postal ballot held in August 2004, two countries that were already members of ICMI, Indonesia and Pakistan, have been admitted to IMU as of January 1, 2005. Consequently at the end of 2005, ICMI had 81 member countries, 67 of which are also members of IMU. Of the 81 member countries of ICMI, 16 had in 2005 no appointed Representative to ICMI: Armenia, Bosnia and Herzegovina, Brunei Darussalam, Estonia, Greece, Kazakhstan, Kuwait, Pakistan, Peru, Saudi Arabia, Senegal, Slovenia, Tunisia, Turkey, Ukraine, Uruguay. (One country, the Democratic Peoples Republic of Korea, has since 2003 an observer status to the IMU.) Among the remaining 65 member countries, 10 could still not be reached by e-mail. During 2005, a total of fifteen collective e-mail messages were sent by the Secretary-General to the ICMI Representatives, some of these providing information on ICMI and its activities, and others asking for input from the Representatives. As indicated in the 2004 report, it was decided that the new election process on which the Executive Committees of IMU and ICMI agreed in 2004 would be used for the 2006 election, but necessarily on an informal basis (pending approval of the new proposed procedures and structures at the 2006 IMU General Assembly). Consequently a Nominating Committee of ICMI was set up for the 2006 election, with a mandate to prepare the selection of the slate of candidates for the ICMI Executive Committee, but operating informally as an advisory body to the IMU Executive Committee. This Nominating Committee is composed of Mogens Niss (Chair), John Ball, Hyman Bass, Victor Vassiliev, Tomas Recio, Gnter Trner and Lim-Teo Suat Khoh. A call for nomination of candidates to the 2007-2009 ICMI Executive Committee was made in August 2005 to the IMU Adhering Organisations and Committees for Mathematics as well as to the ICMI Representatives.


2. ICMEs The composition of the ICME-11 International Programme Committee was finalised early in 2005 and is announced in the June 2005, No. 56, issue of the ICMI Bulletin. The IPC is chaired by Marcela Santilln, Rectora at the Universidad Pedaggica Nacional, and had its first meeting in Mexico City on October 29 to November 1st, 2005. One member of the IPC was denied entrance to Mexico on that occasion, and the President of ICMI wrote to the Mexican Secretary of State to ensure that such a dismissal would not happen again in connection with ICME-11. An official call for bids to host ICME-12 in 2012 was made by the Secretary-General of ICMI during the closing session of ICME-10. This call also appears in the ICMI Bulletin (No. 55, December 2004, pp. 11-12). Three countries, namely (in alphabetical order) China, Korea and South Africa, have responded in 2005 to the invitation of informing the ICMI Executive Committee by a declaration of intent that they are considering preparing an official bid to host ICME-12, to be submitted by November 2006. The preparation of the revised and expanded version of the CD accompanying the book of Proceedings of ICME-9 has met with some delay, so that the diffusion of the new CD, first planned to take place in 2005, has been postponed to 2006. The revised CD will be sent to all ICME-9 participants. 3. ICMI Studies Two new ICMI Studies were launched in 2005: ICMI Study 18: Statistics Education in School Mathematics: Challenges for Teaching and

Teacher Education A new ICMI Study was launched in 2005 on the theme of statistics and is organised jointly with

the International Association for Statistical Education (IASE). The International Programme Committee is chaired by Carmen Batanero and its composition is announced in the December 2005 issue of the ICMI Bulletin. The Study Conference is planned to take place in July 2008 in Monterrey, Mxico, as a satellite conference to ICME-11.

ICMI Study 19: The role of mathematical reasoning and proving in mathematics education The ICMI Executive Committee decided at its December 2005 meeting that the 19th ICMI Study

will be devoted to the role of proofs and proving in mathematics education. The IPC, to be chaired by Gila Hanna and Michael de Villiers, is now under appointment.

As regards other on-going Studies, the situation at the end of 2005 was as follows. ICMI Study 13: Mathematics Education in Different Cultural Traditions: A Comparative Study of

East-Asia and the West The NISS volume is currently in preparation under the editorship of Klaus-Dieter Graf, Frederick

K.S. Leung and Francis Lopez-Real and is expected to appear early in 2006. (NISS 9) ICMI Study 14: Applications and Modelling in Mathematics Education The NISS volume is currently in preparation under the editorship of Werner Blum, Peter Galbraith,

Hans-Wolfgang Hehn and Mogens Niss and is expected to appear by the end of 2006. (NISS 10)


ICMI Study 15: The Professional Education and Development of Teachers of Mathematics The Discussion Document for this Study was published in various journals and newsletters,

including the ICMI Bulletin No. 54, June 2004, pp. 12-23, in LEnseignement Mathmatique 50 (2004) pp. 191-200 and in Educational Studies in Mathematics 56 (2004) pp. 359-372. The Study Conference was held in guas de Lindia, So Paulo, Brazil, on May 15-21, 2005, and was attended by 157 participants (including 94 women) from 33 different countries. The NISS volume is currently in preparation under the editorship of the two co-chairs, Deborah Ball and Ruhama Even. (NISS 11)

ICMI Study 16: Challenging mathematics in and beyond the classroom The two co-chairs of the International Programme Committee are Peter J. Taylor and Edward J.

Barbeau. The Discussion Document for this Study appears in the ICMI Bulletin No. 55, December 2004, pp. 32-46, in LEnseignement Mathmatique 51 (2005) pp. 165-176 and in Educational Studies in Mathematics 60 (2005) pp. 125-139. The Study Conference will take place at the Norwegian University of Science and Technology, in Trondheim, Norway, on June 27 to July 3, 2006.

ICMI Study 17: Digital Technologies and Mathematics Teaching and Learning: Rethinking the Terrain

The two co-chairs of the International Programme Committee are Celia Hoyles and Jean-Baptiste Lagrange. The Discussion Document for this Study appears in the ICMI Bulletin No. 57, December 2005 and in LEnseignement Mathmatique 51 (2005) pp. 351-363. A short announcement was published in Educational Studies in Mathematics 60 (2005) pp. 267-268. The Study Conference will take place at Hanoi University of Technology, Viet Nam, on December 3-8, 2006.

At its June 2003 meeting, the ICMI EC launched a reflection on the ICMI Study programme and its accomplishments since its inception in the mid 1980s. The Studies being concretely reflected in the NISS Study volumes (appearing in the NISS series), the ICMI EC had invited Stephen Lerman (London South Bank University) to review and analyse the research papers published in the Study volumes. The report, received in 2005, suggests some slight modifications in the overall organisation of the Study programme on which the ICMI EC is reflecting. 4. ICMI Regional Conferences Two ICMI Regional Conferences were held in 2005. The First Africa Regional Congress of the International Commission on Mathematical

Instruction was held at the University of the Witwatersrand in Johannesburg, South Africa, on June 22-25, 2005. The conference was attended by some 180 participants from 23 countries, including in particular the following fourteen African countries: Botswana, Burkina-Faso, Kenya, Lesotho, Malawi, Mozambique, Namibia, Nigeria, South Africa, Swaziland, Tunisia, Uganda, Zambia and Zimbabwe. The conference was financially supported by ICMI (3 000 USD) and by IMU Commission on Development and Exchanges (CDE). The latter grant of 10 000 USD allowed to provide support for regional delegates as well as support for two participants from Francophone Africa (Tunisia) and India. A report on the conference appears in the ICMI Bulletin 57 (December 2005).


ICMI-EARCOME 3 (Third ICMI East Asia Regional Conference on Mathematics Education) was held in China from August 7 to 12, 2005. Three higher teacher education institutes were co-organizers: East China Normal University in Shanghai, Nanjing Normal University in Nanjing City, and Hangzhou Teachers college in Hangzhou City. The conference took place during the first four days on the campus of East China Normal University, in Shanghai. Participants then divided into two groups moving to Nanjing or Hangzhou respectively for the last two days sessions. There were over 300 participants, with 152 coming from 15 foreign countries of East Asia and around the world. A report on the conference appears in the ICMI Bulletin 57 (December 2005).

Besides EMF 2006, to take place in May 2006 in Sherbrooke, Canada, two ICMI Regional Conferences are planned for 2007. In addition to ICMI-EARCOME-4 in Penang, Malaysia, already announced, the ICMI EC has granted the status of an ICMI Regional Conference to another conference: Second ICMI Africa Regional Congress, to take place in Nairobi, Kenya, on May 23-27, 2007, on

the theme Embracing Innovative Responses to Challenges in Mathematics Instruction. The ICMI EC is represented on the International Programme Committees of these conferences respectively by Michle Artigue and Bernard R. Hodgson (EMF 2006), Frederick Leung (ICMI-EARCOME 4) and Jill Adler (Second Africa Regional Congress). 5. Other activities The celebration of the centennial of ICMI, in 2008, is now under preparation. As the Commission was established in Italy, during the 1908 Congress of Mathematicians held in Rome, the Executive Committee is grateful that the Italian mathematicians and mathematics educators communities have accepted the task of hosting the symposium to be organised on this occasion. The International Programme Committee in charge of this symposium is chaired by Ferdinando Arzarello and the composition of the IPC is announced in the June 2005, No. 56, issue of the ICMI Bulletin. The symposium will take place on March 5-8, 2008, at the Accademia dei Lincei in Rome. The Local Organising Committee is chaired by Marta Menghini. ICMI has co-sponsored since 2001 international workshops organised in Utah, USA, in the context of the annual Park City Mathematics Institute (PCMI) hosted by the Institute for Advanced Study (Princeton, USA). In 2005 PCMI has supported the participation to the ICMI Study 15 conference on teacher education of two persons involved in the PCMI International Seminar (from Cameroon and Iran). As indicated in the 2004 report, ICMI was invited to join with the organisers of the PCMI International Seminar for a meeting with World Bank officials. In regards to possible actions, recent discussion with PCMI and the World Bank has centred on two projects of joint workshops for training mathematicians and mathematics teachers. One concerns Cambodia and neighbouring countries, in partnership with CIMPA (Centre International de Mathmatiques Pures et Appliques), and the other Africa, in partnership with AMMSI (African Mathematics Millennium Science Initiative). In each case, ICMI is involved in the mathematics teacher education component. Over the last years, ICMI has been sponsoring, jointly with UNESCO and other bodies, the development of a mathematical exhibition entitled Experiencing mathematics, whose aim is to improve the image of mathematics among the general public. Two sets of the exhibit are now


available and are being circulated internationally under UNESCO and ICMI auspices. The 2005 programme of travel included China (Beijing), Greece (Athens), Mozambique (Maputo) and South Africa (Johannesburg, Kimberley, Cape Town, Potchefstroom, Richards Bay). The African exhibition project was supported through a grant of 6 000 USD from IMU Developing Countries Strategy Group (DCSG) which covered the transportation to and from Africa. Additional funds needed to be raised for the circulation of the exhibit inside Africa. The exhibition is devised so to evolve according to the local needs/culture/expertise, for instance by organising a regional and coherent pedagogical design around the exhibition. The Africa exhibits thus incorporated ingredients of ethnomathematics. The current plans for 2006 includes Namibia (12 towns, including Windhoek), Thailand (Bangkok), France (Lyon) as well as Spain (Madrid), where it will be shown during and after the International Congress of Mathematicians in the Centro cultural Conde Duque. ICMI has maintained in 2005 its collaboration to IMU Developing Countries Strategy Group (DCSG) which aims at increasing, guiding and coordinating IMUs activities in support of mathematics and mathematics education in the developing world. ICMI is represented in the DCSG by Vice-President Michle Artigue. ICMI is collaborating to the project of a Clearinghouse for African Mathematics, to be housed at the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy. ICMI contributes to this project by collecting information about activities linked to mathematics education in Africa, in particular as regards existing associations, projects, master and doctorate programmes in education, and mathematics competitions. The DCSG also approved a grant to support the circulation in Africa of the international mathematics exhibition Experiencing Mathematics. 6. IMU Concerns about Mathematics Students Declining numbers of students are choosing to pursue mathematics study at the university level, and many of those who do, even with some initial enthusiasm for mathematics, are discouraged by their early university mathematics instruction and so turn away from it. The resulting decline in the numbers and quality of students pursuing university mathematics studies is a worldwide trend, now for more than a decade, and it threatens the vigour and growth of the mathematical sciences, on which contemporary societies and economies fundamentally depend. The professional mathematics community is not alone in being seriously concerned about this, and this has led the IMU EC to call for a gathering of data to document this trend internationally, and analyze its causes. The IMU has enlisted ICMI to partner in this undertaking, and take responsibility for its design. This trend draws attention to another, distinct but importantly related, problem, which is the inadequate supply of mathematically qualified students choosing to become mathematics teachers in the schools. Thus, gathering data to understand these two parallel phenomena has become the agenda of a joint project of the IMU and ICMI, called the Pipeline Project, which will lead to a report that should be of wide interest, in a number of countries, to mathematics departments, schools of education, government policy and funding agencies, and others. This project was initiated at the July 2004 ICMI EC to which IMU President John Ball participated. A task group, chaired by ICMI EC member Frederick Leung, has been appointed with the mandate to define a detailed work plan for the project and frame it as a proposal for funding to relevant funding agencies. Progress in that direction


has been made in 2005. The Pipeline Project will be organised in collaboration with some major professional organisations. 7. ICMI Affiliated Study Groups ICMI continues to have five Affiliated Study Groups, namely (in the chronological order of their affiliation to ICMI) HPM (The International Study Group on the Relations Between the History and Pedagogy of Mathematics) and PME (The International Group for the Psychology of Mathematics Education) 1976, IOWME (The International Organization of Women and Mathematics Education) 1987, WFNMC (The World Federation of National Mathematics Competitions) 1994 and ICTMA (The International Study Group for Mathematical Modelling and Applications) 2003. 8. The ICMI Awards ICMI Vice-President Michle Artigue is currently chairing the ICMI Award Committee, responsible for selecting the recipients of the Awards. A call for suggestions for the 2005 ICMI Awards has been launched by the Award Committee and disseminated among the mathematics education community though various channels (ICMI Representatives, Affiliated Study Groups, national and international journals and associations). At the end of 2005, the ICMI Awards Committee was completing its review task so that the announcement of the Awards could be made early in 2006. 9. Information and Communication Besides direct e-mail contact with the ICMI Representatives or other members of the international mathematics education community, the dissemination of information about the Commission and its activities is generally accessible through the ICMI Bulletin and the ICMI website, both under the editorship of the Secretary-General of ICMI. During the year 2005, the publication of the Bulletin has experienced delays, so that the two issues dated June 2005 (No. 56) and December 2005 (No. 57) were still outstanding at the time of this report. The ICMI EC has started in 2003 a project of renewing its website (www.mathunion.org/ICMI/) and making a much greater use of it for contacts with the international mathematics education community. An agreement was made in 2005 with the Studio cole of the School of visual arts of Universit Laval for the design and implementation of a new website for ICMI. Bernard R. Hodgson, Secretary-General Universit Laval, Qubec, Canada [email protected] 12 May 2006


ICMI Accounts 2005

1 January 31 December BALANCE AS OF JANUARY 1: ICMI Canadian Dollars 52 210,42 US Dollars 48 510,90 Solidarity Fund (US Dollars) 36 827,13 Canadian Dollars Account: Income: balance 2004 52 210,42 IMU (Schedule A: Administration 15 000,00 CHF) 1) 14 173,93 IMU (Schedule B: Scientific Activities 27 000,00 CHF) 1) 25 513,07 donation to ICMI from the local organizers of Study 15 Conference2) 5 624,28 interest 948,58 total 98 470,28 Expenditure: ICMI Study 15: Study Conference (May 2005), guas de Lindia, travel of IPC2) 3 184,85 ICMI Study 17: IPC meeting, London (April 2004) 3) 418,32 ICMI EC meeting, Copenhagen (July 2004)4) 2 879,87 ICMI EC meeting, Johannesburg (June 2005) 3 840,57 ICMI EC meeting, New Delhi (December 2005) 6 016,61 ICMI Centennial: preliminary meeting, travel and local expenses of Secretary-General5) 1 693,53 ICME-11: IPC meeting, Mxico, October, expenses of Secretary-General 154,02 Klein and Freudenthal ICMI Awards: medals6) 773,04 translation of articles for the ICMI Bulletin 220,00 transfer to USD account (corresponding to 1 160,34 USD) 1 425,37 bank charges (checks and foreign transfers) 94,00 ICMI balance 2005 77 770,10 total 98 470,28


US Dollars Account: Income: ICMI balance 2004 48 510,90 return payment of loan from ICME-107) 7 500,00 donation to ICMI from ICME-108) 2 339,66 transfer from CAD account (corresponding to 1 425,37 CAD) 1 160,34 ICMI interest 744,72 Solidarity Fund balance 20049) 36 827,13 Solidarity Fund interest 497,30 total 97 580,05 Expenditure: ICMI Study 15: Study Conference (May 2005), guas de Lindia, travel of IPC2) 2 390,00 ICMI EC meeting, Johannesburg (June 2005) 2 996,00 ICMI EC meeting, New Delhi (December 2005) 3 970,00 ICMI balance 2005 50 899,62 Solidarity Fund balance 2005 37 324,43 total 97 580,05

Average exchange rate, 2005 1 USD = 1,21 CAD Notes: 1. Considering the fact that the value of the US dollar has in recent years substantially diminished with respect to many currencies, the decision made in 2004 to have the annual grant of IMU given to ICMI in Canadian dollars was maintained in 2005, as this is the currency through which a majority of ICMI expenses are paid. 2. The Local Organising Committee of the conference of the fifteenth ICMI Study on The Professional Education and Development of Teachers of Mathematics, held in guas de Lindia, Brasil, generously supported the participation of the members of the International Programme Committee by covering the local costs of the IPC and also by making a donation of 5 624,28 CAD to ICMI, corresponding almost entirely the travel expenses of IPC members incumbent upon ICMI.


3. Costs, reimbursed only in 2005, for the participation of one member of the International Programme Committee of ICMI Study 17 to the IPC meeting held in London in April 2004. 4. Some of the local costs for the meeting of the Executive Committee of ICMI held in Copenhagen in July 2004 on the occasion of ICME-10 were reimbursed by ICMI in 2005 as part of the final accounting between ICMI and ICME-10. 5. The Secretary-General met in February 2005 with the chair of the International Programme Committee for the celebration of the centennial of ICMI, and other members of the IPC taking part in the Fourth Conference of the European Society for Research in Mathematics Education (CERME 4) in Sant Feliu de Guxols, Spain. 6. In recognition of the work done for ICMI, a student from cole Boulle (Paris), where the medals accompanying the ICMI Awards were designed, was invited to Copenhagen to present the medals to the ICME-10 participants. The local expenses, covered by ICMI, were reimbursed to ICME-10 in 2005 as part of the final accounting between ICMI and ICME-10. 7. Reimbursement in 2005 of an interest-free loan of 7 500 USD made in 2000 to ICME-10. 8. The Local Organising Committee of ICME-10 made in 2005 a generous donation of 2 339,66 USD to ICMI as part of the final accounting between ICMI and ICME-10. 9. The assets of the ICMI Solidarity Fund, established in 1992, are kept, on the ICMI accounts, separately from ICMIs general resources. 10. In addition to generous donations received in 2005 from the organisers of ICME-10 and of the Study Conference of ICMI Study 15, ICMI has been financially supported, directly and indirectly, by various bodies and institutions. In particular the Secretary-Generals home institution, Universit Laval, has contributed in 2005 a substantial support to ICMIs work of the order of 8 000 USD (e.g. through the printing and distribution costs of the ICMI Bulletin, plus a partially reduced teaching load). The same is true of other members of the Executive Committee as well as some of the individuals involved in the programme committee of ICMI activities, as their home institutions could partially cover their travel and other expenses related to their participation in meetings. The ICMI Executive Committee expresses its gratitude for this generous support. However, as already mentioned in previous financial reports, this type of invisible support has become more and more problematic, due to the financial situation of several higher education institutions around the world, thus putting a severe constraint on ICMI finances. Bernard R. Hodgson, Secretary-General Universit Laval, Qubec, Canada 10 May 2006


A Report from HPM

Constantinos Tzanakis

In the last few months there were the following activities, related to the International Study Group on the Relations between the History and Pedagogy of Mathematics (HPM). 1. Mini-Workshop: Studying Original Sources in Mathematics Education Mathematisches Forsschunsinstitut Oberwolfach, Germany, May 1st-5th, 2006, organised by Fulvia Furinghetti, University of Genova, Italy, Hans Niels Jahnke, University of Essen, Germany and Jan van Maanen, University of Groningen, The Netherlands. (This report is based on a more detailed report written by H.N. Jahnke and B. Smestad in the HPM Newsletter, no 62, July 2006.) Among the various possible activities by which historical aspects might be integrated into the teaching of mathematics, the study of an original source is the most demanding and the most time consuming. It requires a detailed and deep understanding of the mathematics in question, of the time when it has been written and of the general context of ideas, and language becomes important in ways which are completely new compared with usual practices of mathematics teaching. Thus, reading a source is an especially ambitious enterprise, but rewarding and substantially deepening the mathematical understanding. In principle, the aims and effects, which might be pursued by way of a source, will not be different from those attained by other types of historical activities. However, there are some ideas, which are specifically supported by reading mathematical sources:

(1) to see mathematics as an intellectual activity; (2) to place mathematics in the scientific, technological and philosophical context of a

particular period in the history of ideas; (3) to participate in an activity oriented more to processes of understanding, than to final

results; (4) to appreciate the role and importance of the different languages involved; those of the

source, of modern mathematics and of everyday life; (5) to see what is supposed to be familiar, becoming unfamiliar;

There have been 17 contributions from 16 contributors coming from 10 different countries, who gave detailed presentations on particular cases concerning the points mentioned above. These presentations were followed by lively discussions, in which participants were given the opportunity to elaborate on their ideas further. Each presentation and the follow-up discussion were based on material (original texts, students worksheets, etc) distributed in advance, or on the spot. 2. Launching a new journal: International Journal for the History of Mathematics Education As mentioned in the previous report on the HPM Group activities (see ICMI Bulletin no 57, December 2005), the rousing success of the Topic Study Group 29, The History of Learning and Teaching Mathematics, at the International Congress on Mathematical Education (ICME-10) in Copenhagen in 2004, demonstrated the need for a permanent and stable international forum for scholarly research in


the history of mathematics teaching. Therefore, a new journal, provisionally titled International Journal for the History of Mathematics Teaching, has been established. More details can be found in the above-mentioned issue of the ICMI Bulletin. In the meantime, the title has been finalized to International Journal for the History of Mathematics Education. It is published electronically by the Teachers College, Columbia University and in printed form by COMAP. The first issue is due for September 2006 and the second for March 2007. Its website (to be updated shortly) is http://www.tc.edu/centers/ijhmt/. 3. The HPM Tongxun and the Tongxun Group in Taiwan (This section is based on a more detailed report written by W-S. Horng which will appear most likely in the HPM Newsletter, no 63, November 2006.) This is a publication in the context of the HPM Group, edited by Wann-Sheng Horng, of the Department of Mathematics of the National Taiwan Normal University. It is published in Chinese since 1998 on a monthly basis. Actually, the February and March issues merge into one issue, and similarly for the July and August issues due to spring and summer vacations respectively. Therefore, the Tongxun has ten issues (both printed and electronic versions) each year and is circulated in printed form of 500 copies to local mathematics teachers and historians of mathematics of the international Chinese community. Several issues are devoted to special themes, like for instance, the special issues:

On the Suan Shu Shu (Han Bamboo Text on Calculation), November 2000; On Arabic mathematics, no 11-12, Vol. 4, 2001; On mathematical induction, no. 2/3, 4, Vol. 7, 2004 (guest editor: Tsang-Yi Lin); On Herons Formula, no. 4, Vol. 9, 2006 (guest editor: Jung-hong Su).

Contributors to this Newsletter are mathematics teachers, postgraduate students or researchers in this area. This collaboration encourages them to promote the HPM activities some of them even become local leaders for both the HPM and Mathematics teaching. They become very enthusiastic about the HPM perspective, contributing to this Newsletter just to share their ideas and vision with their colleagues. Despite the fact that no formal organization, such as a society, is to be expected for up-scaling development, a total of about forty correspondents plus ten editorial members is a strong indication that an active local HPM group could emerge. For instance, some of the members of this group have joined W.S. Horng to write a book on Suan Shu Shu, which is expected to appear in July 2006. For details see http://math.ntnu.edu.tw/~horng/. 4. Proceedings of the ICME-10 Topic Study Group 29: The History of the Teaching and Learning of Mathematics (For more details on this TSG, see the ICMI Bulletin no 55, December 2004, pp. 49-50.) At ICME-10, the first specialized Symposium on the history of mathematics education took place as TSG 29. The Organizing Team was H. Gispert (France), H-C. Hansen (Denmark), H. Khuzwayo (South Africa), G. Schubring (Germany, co-chair) and Y. Sekiguchi (Japan, co-chair), and the main goal of the Symposium was to create a net of international communication between researchers in this


field, and to establish a discussion between the various national histories and their approaches. Directly related to the activities in this TSG is item 2 above in this report. The Proceedings of this TSG will appear as a double issue of Historica Paedagogica, nos 4-5 of vol. XLII (2006). A more detailed report will probably appear in the November issue of the HPM Newsletter (no 63). 5. 5th European Summer University on the History and Epistemology in Mathematics Education (ESU-5), 19-24 July 2007, Univerzita Karlova v Praze, Pedagogick fakulta, Katedra matematiky a didaktiky matematiky (Charles University in Prague, Faculty of Education), Czech Republic (website: http://www.pedf.cuni.cz/kmdm/esu5) This is one of the main activities of the HPM Group. A detailed account of its aim, focus, themes, activities, proceedings and history can be found in the ICMI Bulletin no 57, December 2005. In the mean time the deadline for the submission of proposals has expired (May 15, 2006) and the plenary sessions have been finalized. Activities during the ESU (a) There will be 6 plenary lectures, one for each main theme of the ESU-5: Theme 1 (History and Epistemology as tools for an interdisciplinary approach in the teaching and learning of Mathematics and the Sciences): Leo Corry, Tel-Aviv University, Israel: Axiomatics between Hilbert and R.L. Moore: Two Views on Mathematical Research and their Consequences on Education Theme 2 (Introducing a historical dimension in the teaching and learning of Mathematics): Luis Puig, University of Valencia, Spain: Researching the history of algebraic ideas from an educational point of view Theme 3 (History and Epistemology in Mathematics teachers education): Fritz Schweiger, University of Saltzburg, Austria: The implicit grammar of mathematical symbolism Theme 4 (Cultures and Mathematics): Ulrich Rebstock, University of Freiburg, Germany: Mathematics in the service of the Islamic community Theme 5 (History of Mathematics Education in Europe): Hlne Gispert, Universit Paris-Sud, France & Gert Schubring, Bielefeld University, Germany: The History of Mathematics Education and its contexts in 20th century France and Germany Theme 6 (Mathematics in Central Europe): Magdalena Hyksova, Czech Technical University in Prague, Czech Republic: Contribution of Czech Mathematicians to Probability Theory (b) There will also be 2 panel discussions: Panel 1: Mathematics of yesterday and teaching of today velyne Barbin, Universit de Nantes, France (coordinator); Abraham Arcavi, Weizmann Institute, Israel; Luis Radford, Laurentian University, Canada; Fritz Schweiger, University of Saltzburg, Austria


Panel 2: The emergence of mathematics as a major teaching subject in secondary schools Gert Schubring (coordinator), Bielefeld University, Germany; Livia Giacardi, University of Turin, Italy; Hlne Gispert Universit Paris-Sud, France; Nikos Kastanis, University of Thessaloniki, Greece. (c) There will be parallel sessions of 29 3-hour Workshops, based mainly on historical and/or epistemological material, and another 20 2-hour Workshops, based mainly on didactical pedagogical material. In workshops the participants read and work on the basis of material distributed by the organizer of the workshop (e.g. original texts, chosen and briefly presented by the organizer, or teaching material used or proposed by the organizer etc). (d) There will be 48 30-minute oral presentations, running in parallel sessions, for participants who want to speak about their own experience, or research. This is an activity in the spirit of a conventional research conference. Finally, it is expected that poster sessions and exhibitions of books and other didactical material will also be present in this ESU. 6. Meeting on The promises and problems of a semiotic approach to mathematics, the history of mathematics and mathematics education, July 13-15, 2006, Bielefeld, Germany, organised by Michael Otte, Gert Schubring and Falk Seeger. (This report is an excerpt from a more detailed report written by the organizers and distributed to prospective participants.) During the last two decades or so, the semiotic approach of C.S. Peirce has turned out to be a widely acclaimed framework inspiring the phrasing and the understanding of key problems in the epistemology and history of mathematics. Surprisingly enough, a wide reception of Peirces ideas could also be found in mathematics education possibly as a result of the demise of radical constructivism. It seems appropriate to ask now looking back at what has come out of the promises of the past and what might be lines and key problems of future development. A partial list of some of the salient issues to discuss is the following:

Nominalism and realism of the sign Representation Activity Theory, culture, and semiotics Signs and texts in learning mathematics Symbolization and the process of abstraction in the history of mathematics

More details on the outcome of this meeting will probably appear in the next issues of the HPM Newsletter. 7. A regional meeting related to the HPM Group: Special Meeting on History and Mathematics Education, 14-15 April 2006, University of Thessaloniki, Greece. Motivated by the activities and results of the ICME-10 Topic Study Groups TSG 17 and TSG 29, Greek researchers interested in the HPM perspective organized a regional meeting at the University of Thessaloniki, Greece, aiming to present current international trends on important issues relevant to the


HPM perspective, with reference to all educational levels, and in this way to give an opportunity to the Greek educational community to be informed about those issues that are of great importance nowadays. There were 15 presentations structured along the following three main themes:

On the History of ancient Greek Mathematics (4 presentations) On the History of Mathematics Education (6 presentations) On the relations between History of Mathematics and Mathematics Education (5

presentations). The Proceedings (in Greek) were published in advance by Ziti Publications, Thessaloniki, Greece and were distributed on the spot. A more detailed report will appear in the November issue (No 63) of the HPM Newsletter. 8. Announcement: The former chair of the HPM Group (1996-2000) and co-editor (with the late J.G. Fauvel) of the ICMI Study volume no 6 History in Mathematics Education (Kluwer 2000), Jan van Maanen, started in June 2006 as the Professor of Mathematics Education at the University of Utrecht. As such he will also be the Director of the Freudenthal Institute, a centre of expertise in Mathematics Education, which is part of the Faculty of Mathematics and Sciences of Utrecht University. Constantinos Tzanakis, Chair of HPM Department of Education, University of Crete, 74100 Rethymnon, Crete, GREECE [email protected]

ICMI Affiliated Study Groups Websites The homepages of the five ICMI Affiliated Study Groups are located at the following addresses:

HPM: http://www.clab.edc.uoc.gr/HPM/ ICTMA: http://www.infj.ulst.ac.uk/ictma/ IOWME: http://www.stanford.edu/~joboaler/iowme/index.html PME: http://igpme.org/ WFNMC: http://www.amt.edu.au/wfnmc.html


A Report from WFNMC

Petar S. Kenderov To recognize persons with outstanding contribution to the identification and inspiration of mathematical talent through competitions and related activities, as well as to recognise those who have played a significant role in the development of mathematical challenges with essential impact on mathematics learning, the World Federation of National Mathematics Competitions (WFNMC) regularly (every two years) gives a certain number of awards named after the famous Hungarian mathematician Paul Erds. Paul Erds was born in Hungary (1913). His mathematical talent was identified and developed through mathematics competitions. He influenced a great number of mathematicians by his deep mathematical insight and by disseminating mathematics challenges to researchers in many countries of the world. He authored or co-authored 1500 publications (articles and books) and collaborated with more mathematicians than anyone else. He died in 1996 in Warsaw. According to the regulations of WFNMC, the nominations for this year awards were collected by the Awards Committee (chaired by Professor Peter Taylor, the past President of WFNMC). The Awards Committee assessed the nominations and recommended the candidates for awards to the Executive Committee of WFNMC for making the final decision. The Executive Committee of WFNMC approved the candidates and the Paul Erds Awards for 2006 go to (given in alphabetic order):

Alexander Soifer (USA) Ali Rejali (Iran) Simon Chua (Philippines)

What follows is a brief (and very incomplete!) description of the main contributions of these persons. It reflects partially the report of the Awards Committee. Alexander Soifer is a professor at the University of Colorado at Colorado Springs. His publications include more than 100 articles and four books: Mathematics as Problem Solving (1987); How Does One Cut a Triangle? (1990); Geometric Etudes in Combinatorial Mathematics (1991, with V. G. Boltyanski); and Colorado Mathematical Olympiad: The First Ten Years and Further Explorations (1994). These books are oriented toward helping the students develop their problem solving skills. In a recent list of top 25 articles, most frequently downloaded from the Journal of Combinatorial Theory, Series A, there are three papers where Alexander Soifer is an author or co-author. They are ranked first, third and twenty-first! He is also Editor and Founder of the research quarterly Geombinatorics (since 1991). Alexander Soifer has presented a number of lectures at WFNMC meetings. The topics have covered the four color theorem, contemporary a